𝔖 Bobbio Scriptorium
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Triangles in arrangements of lines

✍ Scribed by G.B. Purdy

Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
486 KB
Volume
25
Category
Article
ISSN
0012-365X

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✦ Synopsis

A set of n nonconcurrent lines in the projective plane (called an arrangement) divides the plane into polygonal cells. It has long been a problem to find a nontrivial upper bound on the number of triangular regions. We show that &n(n -1) is such a bound. We also show that if no three lines are concurrent, then the number of quadrilaterals, pentagons and hexagons is at least cn*.

πŸ“œ SIMILAR VOLUMES

Triangles in arrangements of lines
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✍ D. Eu; E. GuΓ©vremont; G.T. Toussaint πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 436 KB

The envelope of an arrangement of lines is the polygon consisting of the finite length segments that bound the infinite faces of the arrangement. We study the Ε½ geometry of envelope polygons simple polygons that are the envelope of some . arrangement . We show that envelope polygons are L-convex and